In the adjoining figure, chords AC and BD of a circle with centre | Filo
filo Logodropdown-logo

Class 9

Math

All topics

Circles

view icon535
like icon150

In the adjoining figure, chords and of a circle with centre , intersect at right angles at . If , calculate .

Solution:
We know that and are the radius

Base angles of an isosceles triangle are equal 

So we get


Consider

Using the angle sum property 


By substituting the values


On further calculation


By subtraction


So we get


We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by the arc at any point on the circumference

So we get


It can be written as


By substituting the values 


By division 


So we get


In the

Using the angle sum property 


By substituting the values


On further calculation 


By subtraction 


So we get


Therefore ,

view icon535
like icon150
filo banner image

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

playstore logoplaystore logo
Similar Topics
introduction to trigonometry
functions
some applications of trigonometry
quadratic equations
surface areas and volumes